01 - Preheat oven to 350°F. Line an 8-inch round baking pan with parchment paper or grease lightly.
02 - Combine shredded mozzarella and cream cheese in a microwave-safe bowl. Microwave in 30-second intervals, stirring between each, until melted and smooth.
03 - Whisk together almond flour, coconut flour, sweetener, baking powder, and salt in a large bowl.
04 - Add melted cheese mixture and eggs to dry ingredients. Mix with spatula until sticky dough forms. Lightly oil hands if needed for handling.
05 - Place dough between two sheets of parchment paper. Roll into rectangle approximately 1/4 inch thick.
06 - Mix erythritol, cinnamon, and melted butter. Spread evenly over rolled dough surface.
07 - Use parchment paper to assist rolling dough into log from long side. Slice into 8 equal pieces.
08 - Arrange buns cut-side up in prepared pan. Bake 22-25 minutes until golden and set.
09 - Beat cream cheese, butter, powdered erythritol, and vanilla until smooth. Add almond milk as needed for spreadable consistency.
10 - Remove from oven and cool 10 minutes. Spread icing over warm buns before serving.